The patent refers to the loop that holds the medium ring as "attaching means 16" and the loop that holds the small ring as "attaching means 17" (the numbers refer to labels on a diagram). After literally minutes of research, that is the best answer that I can come up with. The patent is available here for your viewing pleasure (as an aside, the USPTO's website kicks ass).

I'm only a wannabe rigger so take this with a grain of salt, but if I found that my risers needed the repairs that you are asking about, I would just buy new ones.